So the beginning of geometry class today just seemed like all the air was sucked out of the room. It was pretty much because I was doing all of the talking. Blah blah blah blah. Or what I was asking them to discuss didn’t resonate with them (“Why is writing mathematics hard? What made doing your formal writing tough?”).
But then I had them try to define some words. Circle. Triangle. Polygon. And they got super animated, most of them. And one girl, when they were working on “circle” excitedly said “I got this” and went to work. So yeah, we’re not done with this yet, but it was great to see that when I get out of their way, and come up with an interesting task, they can get into it.
I also had a nice digression in multivariable calculus today. We were talking about lines. They are 1D creatures that my kids have seen in 2D space. I asked them what the 2D analogue of a line was in 3D space… they said it was a plane. Good. But then one student started talking about how lines have slopes, and so I asked: does a plane have an analogue of slope? What does slope represent in terms of a line? What might make sense in terms of a plane? Their interest seemed piqued. And that’s good enough for me!